Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. #4795 | C7 | direct (N × H) |
| 73. C7×Dic3 | Q16 | semidirect |
| 137. C3×C7 | #462 | semidirect |
| 162. Dic3 | C7×Q16 | semidirect |
| 178. C7 | #4795 | direct (N × H) |
| 191. C3 | C7×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#944 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×Dic12 | 2 |
| C7×#887 | 2 |
| C3×C7×#103 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#810 | 2 |
| C7×#462 | 3 |
| #4795 | 7 |